Other Filters

There are other filters besides the butter worth filter. Some of the main ones are listed below.

• Butterworth

• Chebyshev

• Elliptic

• Bessel

Butterworth

The first, and probably best-known filter approximation is the Butterworth or maximally-flat response. It exhibits a nearly flat passband with no ripple. The rolloff is smooth and monotonic, with a low-pass or highpass rolloff rate of 20 dB/decade (6 dB/octave) for every pole. Thus, a 5th-order Butterworth low-pass filter would have an attenuation rate of 100 dB for every factor of ten increase in frequency beyond the cutoff frequency. It has a reasonably good phase response

Chebyshev

The Chebyshev response is a mathematical strategy for achieving a faster roll-off by allowing ripple in the frequency response. As the ripple increases (bad), the roll-off becomes sharper (good). The Chebyshev response is an optimal trade-off between these two parameters. Chebyshev filters where the ripple is only allowed in the passband are called type 1 filters. Chebyshev filters that have ripple only in the stopband are called type 2 filters , but are are seldom used. Chebyshev filters have a poor phase response. It can be shown that for a passband flatness within 0.1dB and a stopband attenuation of 20dB an 8th order Chebyshev filter will be required against a 19th order Butterworth filter. This may be important if you are using a lower specification processor.

Compared to a Butterworth filter, a Chebyshev filter can achieve a sharper transition between the passband and the stopband with a lower order filter. The sharp transition between the passband and the stopband of a Chebyshev filter produces smaller absolute errors and faster execution speeds than a Butterworth filter.

There are also chebychev type II filters. We wont really discuss that here.

Elliptic

The cut-off slope of an elliptic filter is steeper than that of a Butterworth, Chebyshev, or Bessel, but the amplitude response has ripple in both the passband and the stopband, and the phase response is very nonlinear. However, if the primary concern is to pass frequencies falling within a certain frequency band and reject frequencies outside that band, regardless of phase shifts or ringing, the elliptic response will perform that function with the lowest-order filter.

Compared with the same order Butterworth or Chebyshev filters, the elliptic filters provide the sharpest transition between the passband and the stopband, which accounts for their widespread use.

Bessel

• Maximally flat response in both magnitude and phase

• Nearly linear-phase response in the passband

You can use Bessel filters to reduce nonlinear-phase distortion inherent in all IIR filters. High-order IIR filters and IIR filters with a steep roll-off have a pronounced nonlinear-phase distortion, especially in the transition regions of the filters. You also can obtain linear-phase response with FIR filters.

Filters

All the filters described above may be analogue or digital. However there is a lot of recorded data about the analogue varieties, so it is often the case that designers use the analogue equations and parameters used and convert them to their digital equivalents. There are two main methods for this, namely the Impulse Invariant method and the Bilinear Transform method. We won't discuss this in Circuits II but it's nice to be aware of this as you start to learn digital signal processing.